Homology computations of large cell complexes are often rendered tractable via discrete Morse theory, which provides a principled mechanism for constructing a smaller chain complex with the same homology. The key structure is a partial pairing of the cells. The unpaired cells play the role of critical points and generate the chain groups, while the paired ones furnish a boundary operator. In this talk we will examine a surprising link between discrete Morse theory and the localization of certain poset-enriched categories